Assumptions of the Bell theorem

[Demystifier]

Tumulka's (R4) also seems like a necessary assumption and one that MWI denies:

That's essentially the same as my assumption of macroscopic realism. I don't think it is denied by MWI, but it depends on what one means by "unambiguous". For that matter, I don't think that MWI is a local interpretation, see my https://arxiv.org/abs/1703.08341.

 

[facenian]

Here is our paper on that very topic: Beyond Causal Explanation: Einstein's Principle Not Reichenbach's. For updated details on the physics see: The Relativity Principle at the Foundation of Quantum Mechanics

Already Van Fraassen back in 1982 suggested that quantum correlations don't have causal explanations. He calls realism the existence of such explanations. As far as I know, it is the only way that rejection of realism, to save quantum locality, makes sense.
The widespread belief claiming that since we supposedly need the conjunction of "realism" and "locality" to derive the Bell theorem, therefore, quantum mechanics is local because is not realistic, without euphemisms, can only be catalog as absurd. Why? because ordinary orthodox everyday quantum mechanics is not locality causal and that has nothing to do with the Bell theorem, to begin with. All the Bell theorem tells us is that we cannot restore locality to the quantum theory with non-conspiratorial common causes.
That is why those who really understand what they're talking about when dealing with quantum nonlocality take so seriously superdetemism, for instance, Geradous t' Hooft. I think that we may all agree that he knows what he is talking about when dealing with quantum theory. Why doesn't he reject realism instead? The answer, I am afraid is: because he understands that it would be absurd.
Pardon my insistence but I tried to explain this, a few posts before, and immediately after my post, the next one rejects realism to explain that QM is local.
It is also interesting that an expert in quantum foundations (R. Spekkens) politely called this view(rejection of relism) an ironic mistake (see the discussion between Leifer and Spekkens )

 

[vanhees71]

Already Van Fraassen back in 1982 suggested that quantum correlations don't have causal explanations. He calls realism the existence of such explanations. As far as I know, it is the only way that rejection of realism, to save quantum locality, makes sense.

Do you have a reference?

It's of course a bit strange to say that quantum correlations don't have causal explanations. After all they are described by entangled states, and these must be somehow be prepared (e.g., two polarization entangled photons via parametric downconversion; or as in both the original and Bohm's spin version of the example in the EPR paper via decay of a particle). So there's indeed a causal explanation for the quantum correlations. However the causal explanation is due to the preparation and not due to "spooky actions at a distance" between two well-separated local measurements.

Locality in the sense of "local relativistic QFT", i.e., the microcausality property of local observables is indeed in no contradiction with the observed quantum correlations. After all many of the Bell tests are using photons, and the experiments are all well described by standard QED, which is a local relativistic QFT.

 

[facenian]

Do you have a reference?

It's of course a bit strange to say that quantum correlations don't have causal explanations. After all they are described by entangled states, and these must be somehow be prepared (e.g., two polarization entangled photons via parametric downconversion; or as in both the original and Bohm's spin version of the example in the EPR paper via decay of a particle). So there's indeed a causal explanation for the quantum correlations. However the causal explanation is due to the preparation and not due to "spooky actions at a distance" between two well-separated local measurements.

Locality in the sense of "local relativistic QFT", i.e., the microcausality property of local observables is indeed in no contradiction with the observed quantum correlations. After all many of the Bell tests are using photons, and the experiments are all well described by standard QED, which is a local relativistic QFT.

Van Fraassen, B.C.: The Charybdis of realism: epistemological implications of Bell’s inequality. Synthese 52, 25–38 (1982).
It is written in a philosophical language that for me is hard to read. But is a good example of clear reasoning.

As I see the problem with those claiming that QM is a local theory is that they usually "declare" that QM is local without giving an explanation or rejecting the arguments of those who consider QM as nonlocal (at least of those who claim nonlocality for the correct reasons).

If you need a causal explanation, then you need spooky action. The thing is that QM makes a clear objective prediction; if Alice finds +1 then Bob has to find -1. The orthodox interpretation requires that before the measurement, both particles are in superposition not having a definite value, whence Alice's local measurement has an objective nonlocal effect on far away Bob's laboratory.
This was Einstein's claim, it has nothing to do with determinism or the infamous "elements of physical reality" that he (Einstein) despised. Most importantly, this argument has nothing to do with Bell's theorem in the sense that the problem existed before the Bell theorem was even formulated.
In more formal terms, it can be easily shown that ordinary QM violates local causality as defined by Bell. This is shown, for instance, in section IV of this paper https://arxiv.org/abs/2102.07524v3
Of course, there are correct ways to avoid nonlocality but unfortunately, few working physicists pay much attention to the nonlocality problem and a lot of nonsense is cheerfully declared.
The most common of those is that quantum mechanics is local because the Bel inequality is a classical result. The former argument reveals a complete ignorance regarding the reasons that led Bell to formulate his inequalities in the first place, namely, to explain through non-conspiratorial common causes QM perfect correlations. (The situation is worsened by the introduction of meaningless assumptions like CFD that only contribute to the general confusion, see for instance https://arxiv.org/abs/2012.10238 or https://arxiv.org/abs/1911.00343)
The failure of Bell's common causes program is popularly known as the failure of "local realism" which means that QM nonlocality cannot be fixed by common causes. One the most common blunders associated with this fact is the claim that QM locality is safe thanks to the failure of "local realism" when the actual fact is quite the opposite, failure of local realism only confirms QM nonlocality.
However, as I said before, there are correct ways to avoid QM nonlocality:
* Rejection of a causal explanation
*Superdetemism
*Changing the concept of locality. For instance, replace Bell's local causality with local signaling.
Those are three options I know, there may be others.

 

[vanhees71]

I never understood these arguments. We have a working local theory, relativistic QFT, violating Bell's inequality in all observed cases. The locality of relativistic QFT is built in its foundations. As Weinberg writes in his Quantum Theory of Fields Vol. I: QFT looks as it looks because the assumption of Poincare invariance + locality=microcausality inevitably leads to it.

As I wrote above, you don't need the assumption of acausal spooky actions at a distance when you just take the quantum state (in this case a Bell state) as it is: It's prepared in the very beginning and describes the strong correlations as well as the maximum randomness of the single-particle-observables' values. The correlations are prepared in the very beginning and stay intact until the local measurements made (with registration events space-like separated, so that there cannot be any causal influence of one measurement on the other). So what must be abandoned is the part of Bell's assumption called "realism". From the mathematics I deduce what's meant by "realism" in this case really just is that in fact the measured single-particle observables have determined values before the measurement, and the randomness is just because of our ignorance of the hidden variables, but this assumption is indeed refuted by observation, which all are in accordance with local relativistic QFT.

This philosophical paper is indeed completely incomprehensible to me.

 

[facenian]

I never understood these arguments. We have a working local theory, relativistic QFT, violating Bell's inequality in all observed cases. The locality of relativistic QFT is built in its foundations. As Weinberg writes in his Quantum Theory of Fields Vol. I: QFT looks as it looks because the assumption of Poincare invariance + locality=microcausality inevitably leads to it.

As I wrote above, you don't need the assumption of acausal spooky actions at a distance when you just take the quantum state (in this case a Bell state) as it is: It's prepared in the very beginning and describes the strong correlations as well as the maximum randomness of the single-particle-observables' values. The correlations are prepared in the very beginning and stay intact until the local measurements made (with registration events space-like separated, so that there cannot be any causal influence of one measurement on the other). So what must be abandoned is the part of Bell's assumption called "realism". From the mathematics I deduce what's meant by "realism" in this case really just is that in fact the measured single-particle observables have determined values before the measurement, and the randomness is just because of our ignorance of the hidden variables, but this assumption is indeed refuted by observation, which all are in accordance with local relativistic QFT.

This philosophical paper is indeed completely incomprehensible to me.

I agree, unfortunately, Van Fraassen's rational paper is hard to read (unless perhaps for a trained philosopher). Ironically, he says the same thing as you, that we have a successful working theory and we have to listen to it (but he recognizes that to make QM local, we must give up causal explanations of QM's perfect correlations).
Lamentably, we cannot communicate with each other, or maybe you did not read what I wrote before carefully enough. If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character. This, in principle, has nothing to do with the Bell inequality or realism.
I think that it would be wise to end the discussion right here and accept that QM interpretation is a hard problem.

 

[Fra]

So what must be abandoned is the part of Bell's assumption called "realism". From the mathematics I deduce what's meant by "realism" in this case really just is that in fact the measured single-particle observables have determined values before the measurement, and the randomness is just because of our ignorance of the hidden variables,

I agree with this. The emphasis here is also that it presumes that it's the "physicists" ignorance, and that that the form of the expectation follows the ansatz in bell theorem. But there are perhaps other forms of a sort of "solipsist" HV, that aren't cast into that form.

/Fredrik

 

[martinbn]

If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character.

Because there are no infinite speed signals anywhere in sight.

 

[gentzen]

Because there are no infinite speed signals anywhere in sight.

But there is randomness, and it appears to be nonlocal. Why? Because the randomness only occurs when the entangled particles are measured, and you can compare the random outcomes of the spatially separated measurements later to confirm that they are not independent.

 

[facenian]

Because there are no infinite speed signals anywhere in sight.

That is one of my previously listed solutions: reject Bell's local causality and replace it with local signaling.
However, there are many people that think that is not enough. It does not matter if we are able to build a telephone or not out of those "spooky actions", they exist nonetheless.
It occurs to me that giving up uncontrollable spooky actions as nonlocal effects sounds a little counterintuitive. It is like giving up absolute simultaneity in SR, is how the world is.

 

[Demystifier]

This philosophical paper is indeed completely incomprehensible to me.

Is it a statement about the paper or a statement about you?

 

[vanhees71]

I agree, unfortunately, Van Fraassen's rational paper is hard to read (unless perhaps for a trained philosopher). Ironically, he says the same thing as you, that we have a successful working theory and we have to listen to it (but he recognizes that to make QM local, we must give up causal explanations of QM's perfect correlations).
Lamentably, we cannot communicate with each other, or maybe you did not read what I wrote before carefully enough. If you want to argue for quantum locality you have to explain why ordinary quantum mechanics' objective nonlocal predictions are indeed local, not simply declare their local character. This, in principle, has nothing to do with the Bell inequality or realism.
I think that it would be wise to end the discussion right here and accept that QM interpretation is a hard problem.

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction. There are long-ranged correlations in situations as described by the two-photon Bell states where the single photons' properties are measured at space-like separated events. Within standard relativsitic QFT there cannot be any "spooky action at a distance" influencing the outcome of one of these measurements through the other. Nevertheless standard QFT describes all observations perfectly right. My conclusion from this simply is that we just have to take the quantum state as what it tells us: The probabilities for the outcomes of measurements. In the Bell states the single-photon observables (e.g., polarization which is usually used to demonstrate the quantum features) are maximally indetermined (i.e., the reduced statistical operators describing the single-photon properties are maximum-entropy statistical operators) but at the same time there are strong correlations between the outcomes of measurements. E.g., in the polarization-singlet state, the probability that A finds a H-polarized photon then B must necessarily find a V-polarized photon etc. These strong correlations are then due to the preparation procedure of the photon pair (anyway, operationally it's most plausible to interpret quantum states as a description of the outcome of preparation procedures), i.e., the photon pair has these strong correlations from the very beginning of their creation and, as long as they don't interact with something else on their way to the measurement devices, this correlations are not destroyed.

Of course, there is no causality problem within QM, which is non-relativstic, where actions at a distance are the standard description of interactions anyway. There you can have all kinds of instantaneous-interaction interpretations you like, though for the said photon experiments it's way outside of the realm of its applicability, because, of course, photons cannot be described in any way with a non-relativistic theory.

 

[vanhees71]

Is it a statement about the paper or a statement about you?

About me, of course. I can't even figure out whether I agree or disagree with the author.

 

[vanhees71]

But there is randomness, and it appears to be nonlocal. Why? Because the randomness only occurs when the entangled particles are measured, and you can compare the random outcomes of the spatially separated measurements later to confirm that they are not independent.

The important point is that you can confirm the correlations ONLY later! From an operational/instrumental point of view the locality of relativistic QFT implies the cluster decomposition principle excluding any possibility of faster-than-light communication. So to confirm the correlations "Alice and Bob" have to compare their measurement protocols by exchanging the corresponding information, which is only possible with at most the speed of light.

 

[martinbn]

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction.

In my opinion, it is because the terms "local" and "nonlocal" have more than one meaning. Which changes from paper to paper, and even within one paper. What I don't understand is why people refuse to use a more clear language! Sometimes I think it is on purpose so that the can push their agenda. Sometimes I think it is because they are really bad at philosophy, despite the fact that they put philosophy on a high pedestal.

 

[WernerQH]

Tumulka (https://arxiv.org/pdf/1501.04168.pdf) also discusses many of these assumptions.

Has anyone tried to deny the Reichenbach common cause principle to avoid denying locality? I'm trying to think how that would go...I suppose one could argue that the correlation between two phenomena is just a brute fact with no underlying cause.

I'm wedded neither to locality nor the Reichenbach principle. I think it is futile to seek "explanations" of Bell-type correlations. Rather we should learn to accept them as a fundamental feature of reality, just like we have learned to accept the counter-intuitive constancy of the speed of light. Of course it is a compelling idea that the correlations are caused by "photons" traveling from the source to the detectors. (As compelling as the idea that light waves cannot propagate without an ether!) But it is misleading to think of a photon as an object. It is neither a wave spreading out into space, nor a traveling particle. The only meaning I can give to the term photon is as a pair of short-lived localized currents, which we can call emission and absorption events. I consider myself a realist, but I reject as unreal photons in the sense in which this term is frequently used. What I do think is real are the currents and their statistical tendency to be parallel. That's what photon polarization is about. Also electrons should not be thought of as "objects". Already Heisenberg rejected the notion of an electron's world-line. I think it is more appropriate to think of an electron as a track of short-lived current events in space-time, and of QED as a theory describing the correlations between such events.

Of course there is a strong psychological force against such a world-view. We are very good at detecting correlations, and they can take on a life of their own. Instead of the food, Pavlov's dog reacted to the sound of the bell! Likewise we perceive motion where there are just correlated events. And we assume continuity where there are discrete atoms. To interpolate, we construct continuous fields where there are only discrete events. A gravitational field can make Newton's action at a distance more palatable. Locality is a feature of such fields, but not of the underlying reality. I don't think locality can have a fundamental theoretical status.

PS: Thank you for the reference to the Tumulka paper. I was delighted to read about the GRW "flash" model, and to discover that already John Bell had likened a piece of matter to a "galaxy of events". I'm still not a fan of GRW, because I find it too ad hoc. But it might converge with an effort of interpreting QFT as a statistical theory of events and the correlations between them.

 

[RUTA]

I never understood these arguments. We have a working local theory, relativistic QFT, violating Bell's inequality in all observed cases.

QM is not Lorentz invariant, i.e., QM is the "non-relativistic" limit of QFT, yet it predicts the observed violations of the Bell inequality. Whether or not the parent theory QFT is Lorentz invariant or not is irrelevant. That in a nutshell is the issue.

 

[RUTA]

The situation is worsened by the introduction of meaningless assumptions like CFD that only contribute to the general confusion,

There is a very good reason for talking about counterfactual definiteness (CFD) when discussing the "mystery" of entanglement. Simple hidden variable models will accommodate the correlated outcomes for the same measurements (Mermin's "case (a)"), so the real "mystery" resides in the correlations found in different measurements (Mermin's "case (b)"). And that "mystery" comes from assuming the simple hidden variable account responsible for the case (a) outcomes obtains counterfactually for case (b), i.e., the quantum state doesn't "know" how it will be measured, so it has to be ready for case (a). But being ready for case (a) then does not yield the correct correlations for case (b) if there is no superluminal communication between measurement events. That's Mermin's presentation.

 

[facenian]

Thanks for the reference, it is facinating! However I was strictly talking about CFD as used to derive the Bell inequality.

 

[facenian]

QM is not Lorentz invariant, i.e., QM is the "non-relativistic" limit of QFT, yet it predicts the observed violations of the Bell inequality. Whether or not the parent theory QFT is Lorentz invariant or not is irrelevant. That in a nutshell is the issue.

I would add that Lorentz invariant does not imply a velocity limit. That only works the other way around.
That QFT is local by construction sounds very dubious to me. It is only Lorentz invariant by construction.

 

[Demystifier]

I would add that Lorentz invariant does not imply a velocity limit. That only works the other way around.
That QFT is local by construction sounds very dubious to me. It is only Lorentz invariant by construction.

Indeed, there are many effective non-local Lorentz invariant QFT theories, such as those involving $\Box^{-1}$ in the action.

 

[vanhees71]

I'm wedded neither to locality nor the Reichenbach principle. I think it is futile to seek "explanations" of Bell-type correlations. Rather we should learn to accept them as a fundamental feature of reality, just like we have learned to accept the counter-intuitive constancy of the speed of light.

In addition, we have a perfect "explanation" (I'd rather say "theoretical description") of Bell-type correlation: Quantum theory. I also don't know, whether Reichenbach's ideas help much. I've the impression they make already special relativistic classical physics more complicated than necessary.

 

[Lynch101]

My problem is to understand, why people think relativistic quantum field theory were not local although it's local by construction.

My conclusion from this simply is that we just have to take the quantum state as what it tells us: The probabilities for the outcomes of measurements.

From reading and listening to various viewpoints (here and elsewhere) it seems to me that there are two levels to the discussion which can lead to people talking past each other. To my mind, the issue lies in the question of 'completeness'.

Those that argue that QM or QFT must be non-local seem to be taking the position that a complete description of physical reality, in the broader sense meant by EPR, must be non-local to explain how the observed correlations occur i.e. what underlying mechanism gives rise to such correlations.

While QFT might be local by design, if the mathematics only gives us 'the probabilities for the outcomes of measurements', then it can't be a complete description of physical reality.

This is what Lee Smolin has said about 'going beyond the statistical predictions of QM'.

 

[vanhees71]

But the local explanation of how the observed correlations occur is given by Q(F)T: It's due to the preparation of the system.

You also cannot conclude from the fact that Q(F)T gives "only" probabilities for the outcomes of measurments, that it must necessarily be an incomplete theory. It may well be that Nature really behaves inherently probabilistic. We don't know this, of course, but there is no empirical evidence for determinism.

 

[Lynch101]

But the local explanation of how the observed correlations occur is given by Q(F)T: It's due to the preparation of the system.

You also cannot conclude from the fact that Q(F)T gives "only" probabilities for the outcomes of measurments, that it must necessarily be an incomplete theory. It may well be that Nature really behaves inherently probabilistic. We don't know this, of course, but there is no empirical evidence for determinism.

But, if Q(F)T only gives probabilities for the outcomes of measurments then, by definition, the mathematics doesn't describe the system prior to measurement. This would mean that it cannot be a complete description of physical reality.

 

[vanhees71]

But it describes the system prior to measurement. Knowing the quantum state doesn't imply that all observables take predetermined values. According to all observations known, particularly those very precise ones with Bell states, that's really the case.

 

[martinbn]

But, if Q(F)T only gives probabilities for the outcomes of measurments then, by definition, the mathematics doesn't describe the system prior to measurement. This would mean that it cannot be a complete description of physical reality.

You are making assumptions on how reality should be. If you prepare a system and make a measurment, and you do that many times in the exact same way, but get differnt results, how can you expect to predict anything more than probabilities? Of course it may be that the preparations were not identical, but we don't know, so your demand for more is based on an assumption. Also the fact that decades of refining and improveing the expariments have shown no improvement for the probabilities, say what used to be 50-50 now is 51-49, is a good indication that may be nature is like that and you cannot complete the theory in that direction.

By the way that is not what EPR meant by incompletenes.

 

[Lynch101]

But it describes the system prior to measurement. Knowing the quantum state doesn't imply that all observables take predetermined values. According to all observations known, particularly those very precise ones with Bell states, that's really the case.

It doesn't require that all observables take pre-determined values, but if the mathematics gives us the probability distribution for the outcome of a position measurement, it doesn't tell us where it was prior to measurement.

While it might be a classical bias to expect a definite value for position, prior to measurement, the system in question must be somewhere as it cannot be nowhere. If the mathematics doesn't describe this 'somewhere' it cannot give a complete description of physical reality.

Some interpretations ascribe an ontology to the wave function which attempts to describe this 'somewhere', which make them [an attempt at] a complete description of physical reality. Any interpretation that only gives probabilistic predictions for the outcomes of measurements cannot be said to describe the location of the system prior to measurement. Since the system must be somewhere - even if that doesn't imply a definite location - such an interpretation/theory cannot be said to be a complete description of physical reality.

 

[vanhees71]

No, it doesn't tell us where it was prior to measurement, but not because it's an incomplete description, but because indeed the position was indetermined. Then the probabilistic description is complete. I still don't know your definition of "physical reality".

 

[Lynch101]

You are making assumptions on how reality should be. If you prepare a system and make a measurment, and you do that many times in the exact same way, but get differnt results, how can you expect to predict anything more than probabilities? Of course it may be that the preparations were not identical, but we don't know, so your demand for more is based on an assumption. Also the fact that decades of refining and improveing the expariments have shown no improvement for the probabilities, say what used to be 50-50 now is 51-49, is a good indication that may be nature is like that and you cannot complete the theory in that direction.

By the way that is not what EPR meant by incompletenes.

According to EPR, a complete theory is one in which 'every element of the physical reality must have a counterprart in the physical theory.

Quantum systems must be located somewhere [in the universe] prior to measurement, since they cannot be 'nowhere'. If the mathematical formalism only gives the probabilities for observing the quantum system at a given location after interacting with a measurement device, then it does not describe the location of the system prior to that. Since it must be located 'somewhere', any such interpretation/theory cannot be considered a complete description of physical reality.

 

[martinbn]

According to EPR, a complete theory is one in which 'every element of the physical reality must have a counterprart in the physical theory.

Quantum systems must be located somewhere [in the universe] prior to measurement, since they cannot be 'nowhere'. If the mathematical formalism only gives the probabilities for observing the quantum system at a given location after interacting with a measurement device, then it does not describe the location of the system prior to that. Since it must be located 'somewhere', any such interpretation/theory cannot be considered a complete description of physical reality.

That is not EPR, it is your statement. EPR say that if you can predict with 100% certainty the outcome of a measument, then a complete theory must accout for that, the observable must have a value before the measurement. What you are saying is that the system must be somewhere (because it cannot be nowhere), therefore any complete theory must have values for positions at any time.

 

[Lynch101]

No, it doesn't tell us where it was prior to measurement, but not because it's an incomplete description, but because indeed the position was indetermined. Then the probabilistic description is complete. I still don't know your definition of "physical reality".

I'm referencing the "physical reality" of the EPR paper. I take it to mean 'the Universe' or 'how the universe is'.

The system must be located somewhere in the universe prior to measurement. If it were not, then it couldn't interact with the measurement device in the first place. If all we have is the probability of observing the system in a given location after its interaction with the measurement device, then we lack a description of where the system is located prior to measurement. It may not necessarily require a definite value, but it does require a description for a theory to be considered a complete description of physical reality.

 

[Lynch101]

That is not EPR, it is your statement.

Whatever the meaning assigned to the term complete, the following requirement for a complete theory appears to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness.

EPR paper

EPR say that if you can predict with 100% certainty the outcome of a measument, then a complete theory must accout for that, the observable must have a value before the measurement.

Yes, EPR did say that, but they also said that was just one possible way, not the only possible way.

It seems to us that this criterion, while far from exhausting all possible ways of recognizing a reality, at least provides us with one.

What you are saying is that the system must be somewhere (because it cannot be nowhere), therefore any complete theory must have values for positions at any time.

I'm not suggesting the theory must have definite values, but it must have some description of its location - whatever form that may take.

A theory/interpretation which only gives the probability of a location after interacting with a measurement device does not, by definition, describe the location prior to measurement. Thus making it, by definition, an incomplete description of physical reality.

 

[WernerQH]

The system must be located somewhere in the universe

It is a natural assumption that a "system" is alwas there. But it still is an assumption. It is silly to question it in the case of the moon. At least in some sense it is always there. But it is it an irrefutable fact in the case of "objects" like electrons and photons?

H.G. Wells wrote:
"It may be that we exist and cease to exist in alternations, like the minute dots in some form of toned printing or the succession of pictures on a cinema film."
(Science and Ultimate Truth, 1931)

Wells obviously had a more general notion of "system".

 

[vanhees71]

That quantum systems are located somewhere is described by QT in the sense that the probability that the particle is somewhere is 1 (supposed it is sure that it is indeed still there and not annihilated with some antiparticle).